I wish I could show you a drawing, but here goes:

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The angle sides and the bottom are all of length one. We want to maximize area which we can split into three parts:

Triangular cross sectional areas on the sides of the gutter, and the middle square c-s area. For some angle, , the height is and the top "length" is . The area of such triangle is . The area of the square is . Add up the areas to get:

To maximize the area, we need to take the derivative w.r.t. theta and set it equal to zero.